Pyramidal n-gon
The base of a pyramid has n edges. What is the difference between the number of edges the pyramid has and the number of faces the pyramid has?
Age
14 to 16
Challenge level
Problem
The base of a pyramid has $n$ edges. In terms of $n$, what is the difference between the number of edges of the pyramid and the number of faces?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
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Therefore there are $2n$ edges in total.
There are also $n$ faces that meet at the apex of the pyramid, and one more for the base, so a total of $n+1$ faces.
Therefore the difference is $2n - (n+1) = n-1$.